3.1.1 X-ray diffraction (XRD)
X-ray diffraction (XRD) is a non-destructive technique that reveals detailed information about the crystallographic structure of natural and manufactured materials.
It’s now a common technique for the study of crystal structures and atomic spacing.
When a monochromatic X-ray beam with wavelength λ is projected onto a crystalline material at an angle θ, diffraction occurs only when the distance traveled by the rays reflected from planes differs by a complete number n of wavelengths when conditions satisfy Bragg's Law (nλ=2d sin θ). This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample.
Conversion of the diffraction peaks to d-spacing allows identification of materials. By varying the angle, the Bragg's Law conditions are satisfied by different d-spacings in polycrystalline materials. Based on the principle of X-ray diffraction, a wealth of structural, physical and chemical information about the material investigated can be obtained. A host of application techniques for various material classes is available, each revealing its own specific details of the sample studied.
The specific wavelengths are characteristic of the target material (Cu, Fe, Mo, Cr). The geometry of an X-ray diffractometer is such that the sample rotates in the path of the collimated X-ray beam at an angle θ while the X-ray detector is mounted on an arm to collect the diffracted X-rays and rotates at an angle of 2θ. The instrument used to maintain the angle and rotate the sample is termed a goniometer. X-ray powder diffraction is the method used for the identification of unknown crystalline materials. In our results, the XRD is performed by the PANalytical X'Pert PRO analysis system.
3.1.2 Scanning electron microscope (SEM)
The scanning electron microscope (SEM) is a type of electron microscope that images the sample surface by scanning it with a high-energy beam of electrons in a raster scan pattern. The electrons interact with the atoms that make up the sample producing signals that contain information about the sample's surface topography, composition and other properties such as electrical conductivity.
The types of signals produced by an SEM include secondary electrons, characteristic x-rays, specimen current and transmitted electrons. These types of signal all require specialized detectors for their detection that are not usually all present on a single machine. The signals result from interactions of the electron beam with atoms at or near the surface of the sample. In the most common or standard detection mode, secondary electron imaging or SEI, the SEM can produce very high-resolution images of a sample surface, revealing details about 1 to 5 nm in size.
Due to the way these images are created, SEM micrographs have a very large depth of field yielding a characteristic three-dimensional appearance useful for understanding the surface structure of a sample. This is exemplified by the micrograph of pollen shown to the right. A wide range of magnifications is possible, from about x 25 (about equivalent to that of a powerful hand-lens) to about x 250,000, about 250 times the magnification limit of the best light microscopes. Characteristic X-rays are emitted when the electron beam removes an inner shell electron from the sample, causing a higher energy electron to fill the shell and release energy. These characteristic x-rays are used to identify the composition and measure the abundance of elements in the sample. The morphology and geometry dimensions of our samples are determined with models Hitachi S-4200 FESEM and Horeba EX-220 energy dispersion spectroscopy.
3.1.3 Magnetic Property Measurement System (MPMS)
The Quantum Design MPMS provides solutions for a unique class of sensitive magnetic measurements in key areas such as high-temperature superconductivity, biochemistry, and magnetic recording media. The modular MPMS design integrates a Superconducting Quantum Interference Device (SQUID) detection system, a precision temperature control unit residing in the bore of a high-field superconducting magnet, and a sophisticated computer operating system. Powerful software controls measurements, making data collection and analysis quick and easy.
3.1.4 Physical Property Measurement System (PPMS)
The Quantum Design PPMS represents a unique concept in laboratory equipment:
an open architecture, variable temperature-field system, designed to perform a variety of automated measurements. Use the PPMS with options designed for it or easily adapt it to your own experiments. Sample environment controls include fields up to
± 5 Tesla and temperature range of 1.8 - 400 K. Its advanced expandable design combines many features in one instrument to make the PPMS the most versatile system of its kind.
3.1.5 Cryostat system
The construction for temperature control system include three main parts, the OXFORD Heliox series 3He refrigerator, sample holder, and control device. The figure below represents a schematic of the. The 3He refrigerator insert can be treated like any sample rod for a variable temperature insert. Once loaded, the insert is cooled from 300K down around 70K using exchange gas. The 3He gas contained in a small dump sitting on top of the insert is then condensed at around 1.5K. Once the
3He pot has reached a stable temperature and condensation is completed, the adsorption pump will start to cool the 3He pot and experimental set-up to below 300 mK. The condensation and the cool down time typically require less than 1 hour.
Meanwhile, a homemade sample holder (Figure 3.1) was mounted together with the commercial heater on the 3He pot. The minimum temperature of this construction is 0.4 K, and in our experience, the temperature of sample can keep at this temperature over 4 hours. Furthermore, the whole temperature control instruments were monitored by a computer through the interface GPIB.
Radiation Shielding
Sample chip
Sample mounting bas
Copper base
Figure 3.1 The sketch of the homemade sample holder with copper base and two layer shields.
3.2 Electronic property measurement methods
3.2.1 Four-probe method
If you wanted to determine the high precise of a resistance, you would probably connect its two leads up to an Ohmmeter and read off the value. This could be a problem, if the resistance you are trying to measure is very small. A voltage source may damage your sample due to the high passing current. Do you know how much current should we use to measure resistance? For this reason, one often determines the resistance of a sample by passing through it a known current I, measuring the resulting voltage drop ΔV, and performing the division to get R = ΔV/I. This might be a direct current, or it might be an alternating current. The constant-current circuit allows us to determine the sample resistance with a very small current eliminating the possibility of damage to the sample, especially for an ultra fine wire.
We now turn to the other issue, the problem of lead resistance. The sample resistance might be so low that the resistance of the leads running to the sample might be significant by comparison. A related problem is that of contact resistance.
Somehow we must connect leads between our sample and the external circuit, and this involves making "contact" to the sample. Contacts are notorious sources of resistance. The situation is illustrated as Figure 3.2a. Let the two contacts to the sample be represented by equivalent resistances RC1 and RC2. The measured voltage drop V = I (RC1 + RS + RC2). How do we know what fraction of the voltage drop V is due to R and how much is due to the contacts? Fact is we have no way of knowing, because we measure their series combination. This is especially a problem if RS is much smaller than RC1 and RC2. Consequently, the resistance of the leads will be in series with the resistance you are trying to measure, so will of course
include to the reading.
The four-probe method is the most common way to separate out the resistivity of conducting materials. This can be seen by looking at the equivalent circuit, shown in the Figure 3.2b. Two of the probes are used for applied current source and the other two probes are used to measure voltage. By separating the current contacts from the voltage contacts we are able to distinguish the sample resistance from that of the contacts and connecting wires. If the voltmeter has an infinite input impedance, no current will flow through the voltage contacts, and the measured voltage drop V is across the portion of the sample that is between the two voltage contacts. Even if R is much smaller than RC1 and RC2, the measured voltage drop is still V = I R.
(a)
Figure 3.2 The sketch for the conditions of leads connection from sample to instruments and the effective circuits. Inset (a) is the 2-probe method. Inset (b) is the 4-probe method.
Using a Lock-in to Measure Resistance
The voltage drop ΔV is measured with an oscilloscope, high sensitive voltmeter, or better yet, with a lock-in amplifier. If you are trying to measure voltages on the order of microvolt, you should consider using a lock-in amplifier. Lock-in amplifiers are ideal for making low-frequency resistance measurements. The basic idea is to replace the direct current source with an oscillator I0sinωt, and to replace the voltmeter with a phase-sensitive-detector. Most lock-in amplifiers combine both of these. The oscillator frequency ω is set to some low value, say 13 Hz. The lock-in is set to use its own internal oscillator as the reference for the PSD. The lock-in is calibrated to read ΔV in RMS-voltage so that the sample resistance R=ΔV/I=(ΔV/ERMS)×RL, where ERMS and RL is the RMS-voltage of the lock-in’s oscillator and a series resistor, respectively. In the circuit above there is an oscilloscope connected to the signal monitor output of the lock-in. It is very important to "look" at what it is that you are measuring; never trust the reading without first viewing the signal. The BNC cable connections are "blown up" on the sample box to show the internal wiring of the box. To be sure, all BNC connectors are connected to the BNC cables as expected.
3.2.2 Self-heating 3ω method
Knowledge of the thermal conductivity of thin films, multilayer thin-film, and wires structures is critical for a wide range of applications in microelectronics, photonics, microelectromechanical systems, and thermoelectric materials [44-47].
Some methods developed for the determination or measurement of thermal conductivity of materials, such as the steady-state technique, the 3ω technique, and the thermal diffusivity measurement. [48] Each of these techniques has its own advantages as well as its inherent limitations, with some techniques more appropriate to specific sample geometry, such as the 3ω technique for individual nanowires. For steady-state method, the thermal conductivity of solids is usually determined by measuring the temperature gradient produced by a steady heat flow in a one-dimensional geometry. Direct measurements of the thermal conductivity, for example, typically require the determination of the heat flux and the temperature drop between two points of the sample. Figure 3.3 shows a typical sample configuration of a bulk system. Unfortunately, these techniques often require large, precisely shaped samples and extreme care to be used successfully. From a practical view, it’s impossible to achieve this setup for thin-film and nanowire system. In order to study thin-film and nanowire system, a technique was developed to measure thermal properties. One important technique is the 3ω method, which take 3rd harmonic signal to measure the thermal and electrical conductivity along longitudinal direction.
The 3ω technique and methods for the measurement of thermal conductivity of nanowires is discussed in detail as follow.
In this method, if the sample is electrically conductive and with a temperature-dependent electric resistance, the specimen itself could serve as a heater as well as a temperature sensor. Feeding an ac electric current of the form I0sinωt
into the specimen creates a temperature fluctuation on it at the frequency 2ω, and accordingly a resistance fluctuation at 2ω. This further leads to a voltage fluctuation at 3ω across the specimen. Systematic investigations of the 3v method were carried out mainly during the 1960’s [49-51] and in the last ten years, [52-57] which made the method practical. However, in the previous studies the heat conduction equation was solved under the approximations either only for the high frequency limit, [49, 50, 57] or only for the low frequency limit. [52, 54, 55] With those approximations one lost either the information on the thermal conductivity or the information on the specific heat of the specimen. By comparison with other methods, the 3ω method yields more information. This method can measure electrical conductivity (σ), thermal conductivity (κ) and specific heat (Cp) at the same time. In following sessions the explicit solution for the 1D heat-conduction equation, which was reported by L. Lu in [58] would discuss.
ΔT
Heat sink
Sample Heater
Figure 3.3 The typical arrangement for thermal conductance measurement.
Usually, the large bulk sample is fixed on a high thermal conductive heat sink. The heater is placed on top of sample to provide a steady heat flow by a power P, which generate a stable temperature gradient cross the sample. The temperature different ΔT then is measured with a set of thermometry, since the thermal conductivity κ can be calculate with the simple formula κ=P/ΔT.
We consider a uniform filament-like specimen in a four-probe configuration as for electrical resistance measurement. A complete construction for this model is shown in Figure 3.4. The two outside probes are used for feeding an electric current, and the two inside ones for measuring the voltage across the specimen. The specimen between the two voltage probes is suspended to allow temperature fluctuation. All probes have to be highly thermal conductive, to heat link the specimen at these points to the substrate. The specimen has to be maintained in a high vacuum and the whole setup is heat shielded to the substrate temperature to minimize the radial heat loss through convection and radiation. In such a configuration and with an ac electrical current of the form I0sin(ωt) passing through the specimen, the heat generation and diffusion along the specimen can be described by a partial differential equation, which the details will descript in next session.
Heat sink L
Δ
0 L
Figure 3.4 the sketch for sagging structure and the temperature distribution of a wire. As shows in the right figure, a sagging wire presents a temperature gradient by injecting a current into wire. For an appropriate applied current, the temperature of end points of the wire contacting with heat sink is keeping the same with heat sink.
3rd harmonic signal:
In a one-dimensional configuration and with a sinusoid electrical current passing through the specimen, the heat generation and diffusion along the specimen can be described by the following partial differential equation and the initial and boundary conditions:
where κ, Cp, R, ρ, L, and S are the thermal conductivity, specific heat, electric resistance, mass density, length, and cross-section of the specimen at the substrate temperature T0 , respectively. Let Δ(x, t) denote the temperature variation from T0, i.e., Δ(x,t)=T(x,t)-T0 Eqs. 3.1 then becomes
They obtain the temperature distribution along the specimen:
( ) ( )
accumulation at the center of the specimen. Δ0 is only κ dependent. The information of CP is included in the fluctuation amplitude of the temperature around the dc accumulation.By solving the partial differential equation, the resistance fluctuation can be expressed as
The production of the total resistance R+δR and the current I0 sinωt, the voltage across the specimen contains a 3ω component V (t). Only taking the n=1 term at
low frequency range, the 3ω component can be express as
The root-mean-square value of voltage across the specimen contains a 3ω component V3ω(t), we have
where the κ and γ are thermal conductivity and thermal time constant, respectively.
By fitting the experimental data to this result, we can get the thermal conductivity and thermal time constant of the specimen. The specific heat can then be calculated as Cp=π2γκ/ρL2.
3.2.3 Electronics and sample chip
The measurement system for four-probe and self-heating method includes three main parts; sample temperature control and electronic measurement system.
For the sample temperature control, a sample holder from THERMODYNAMIC INSTRUMENTS CORP. with low magnetic field NiCr-heater was mounted onto the commercial cryostat (OXFORD He3 refrigerator), which provide a cooling power to cool sample to low temperature. The heating power was controlled by the temperature controller LakeShore-340 of Lake Shore Cryotronics, Inc., which control the temperature of sample in the range form 0.3 to 350 K. In the holder, there were three resistance-temperature-detector (RTD) used to detect the temperature of sample.
They are PT100 and Cernox from Lake Shore Cryotronics, Inc., and SA-1400 from THERMODYNAMIC INSTRUMENTS CORP. PT100 perform an accuracy temperature sensing in the calibrated range from 30 to 550 K, however, Cernox and SA-1400 give the accuracy temperature from 0.3 to 100 K. Especially, the calibrated SA-1400 temperature sensor is a high sensitivity and low magnetic influence sensor, which provide a double checking to prevent the missing working of Cernox.
Furthermore, this whole set was installed to a He4 dewar, which includes a superconductor magnetic with maximum field up to 9 Tesla.
The electronic instruments for resistance measuring include an alternating current source, preamp and lock-in amplifier, and power transformer. The model of current source was KEITHLEY 6221, which provide sine wave current from 1 nA to 100 mA and frequency range from 1 mHz to 100 kHz. The voltage signal were amplified by pre-amplifier 5113 and pick up with lock-in amplifier AMetek model 7265. All instruments operating were performed by a computer with GPIB and LABVIEW program. Meanwhile, all data were collected and transfer to computer
for recording and calculating by GPIB interface. The characterization and operating detail of cryostat probe was described in session 3.1-D. The detail schema of the temperature control devices and electronic instruments show in figure 3.5.
Trigger AC current source
LOCK-IN amplifier
Heat sink
High thermal
conductive substrate
4- probe electrodes
Figure 3.5 The schematic sketch of measurement setup and settling of specimen.
Chapter 4
Nanowires fabrication
Introduction
First of all, the fabrication of nano-scale materials is a challenge and much important to research of low-dimensional systems. This chapter introduces the experimental tools and techniques involved in fabricating nanowires. In order to synthesis nano-materials, several methods were reported to form nanostructure.
Some of them, the methods are used usually for some special materials. This chapter introduces two methods to fabricate nanowires. The first part is a Bottom-up method, which the nanostructure formed self-assembly (Self-assembly method, SAM). Section 4.1 describes the detail procedures to fabricate nano-porous template and how to form nanowires within these anodic aluminum oxide (AAO) templates. The second part is a Top-down method, which need a lot of patterning and etching processes. Sections 4.2 will give the description to the lithographic (Optical Lithography, OL and Electron Beam Lithography, EBL), film deposition and etching techniques.
4.1 Bottom-up method
In this method, we combined two techniques to form nanowires. First, we use the anodization process to form porous template, it’s so called anodic aluminum oxidation technique. This technique is a self-assembly reaction, the acid solution will oxidize aluminum (Al) foil under a specific applied electric field to form amorphous alumina (Al2O3) with high aspect ratio and uniform nano-pores. Second, a deposition procedure is used to grow materials into these nanopores in templates by so called electrodeposition.
4.1.1 Fabrication of nano-scale porous template
In recent years, there has been increasing interest in the fabrication of nanometer-sized fine structures because of their potential utilization in electronic, optical, and micromechanical devices. Although, Several techniques have been proposed to synthesis high-density and regular nano-pore arrays, such as e-beam and x-ray lithography, proton beam writing (PBW) and AAO [59-65]. The AAO is one
In recent years, there has been increasing interest in the fabrication of nanometer-sized fine structures because of their potential utilization in electronic, optical, and micromechanical devices. Although, Several techniques have been proposed to synthesis high-density and regular nano-pore arrays, such as e-beam and x-ray lithography, proton beam writing (PBW) and AAO [59-65]. The AAO is one